Related papers: Hypothesis testing for partial tail correlation in…
A bivariate random vector can exhibit either asymptotic independence or dependence between the largest values of its components. When used as a statistical model for risk assessment in fields such as finance, insurance or meteorology, it is…
Despite the successes of probabilistic models based on passing noise through neural networks, recent work has identified that such methods often fail to capture tail behavior accurately, unless the tails of the base distribution are…
In this study, a path-based Statistical Static Timing Analysis (SSTA) is formulated as a problem within the statistics of correlated extremes. For extreme value statistics with correlations, a novel approach to studying such systems, when…
Extreme weather events are becoming more frequent and intense, posing serious threats to human life, biodiversity, and ecosystems. A key objective of extreme event attribution (EEA) is to assess whether and to what extent anthropogenic…
Estimation of tail quantities, such as expected shortfall or Value at Risk, is a difficult problem. We show how the theory of nonlinear expectations, in particular the Data-robust expectation introduced in [5], can assist in the…
Spatial modelling of extreme values allows studying the risk of joint occurrence of extreme events at different locations and is of significant interest in climatic and other environmental sciences. A popular class of dependence models for…
We demonstrate both analytically and numerically that the existing methods for measuring tail dependence in copulas may sometimes underestimate the extent of extreme co-movements of dependent risks and, therefore, may not always comply with…
We examine statistical pictures of violent conflicts over the last 2000 years, finding techniques for dealing with incompleteness and unreliability of historical data. We introduce a novel approach to apply extreme value theory to…
The concept of intermediate tail dependence is useful if one wants to quantify the degree of positive dependence in the tails when there is no strong evidence of presence of the usual tail dependence. We first review existing studies on…
A scan statistic is examined for the purpose of testing the existence of a global peak in a random process with dependent variables of any distribution. The scan statistic tail probability is obtained based on the covariance of the moving…
The extreme value theory is very popular in applied sciences including Finance, economics, hydrology and many other disciplines. In univariate extreme value theory, we model the data by a suitable distribution from the general max-domain of…
We show bounds on tail probabilities for quadratic forms in sub-gaussian non-necessarily independent random variables. Our main tool will be estimates of the Luxemburg norms of such forms. This will allow us to formulate the above-mentioned…
Risk measures like Marginal Expected Shortfall and Marginal Mean Excess quantify conditional risk and in particular, aid in the understanding of systemic risk. In many such scenarios, models exhibiting heavy tails in the margins and…
Copulas provide an attractive approach for constructing multivariate distributions with flexible marginal distributions and different forms of dependences. Of particular importance in many areas is the possibility of explicitly forecasting…
We propose a semiparametric method for fitting the tail of a heavy-tailed population given a relatively small sample from that population and a larger sample from a related background population. We model the tail of the small sample as an…
Max-stable processes have proved to be useful for the statistical modelling of spatial extremes. Several representations of max-stable random fields have been proposed in the literature. For statistical inference it is often assumed that…
We consider the estimation of large covariance and precision matrices from high-dimensional sub-Gaussian or heavier-tailed observations with slowly decaying temporal dependence. The temporal dependence is allowed to be long-range so with…
We investigate a family of discrete-time stationary processes defined by multiple stable integrals and renewal processes with infinite means. The model may exhibit behaviors of short-range or long-range dependence, respectively, depending…
For the problem of estimating lower tail and upper tail copulas, we propose two bootstrap procedures for approximating the distribution of the corresponding empirical tail copulas. The first method uses a multiplier bootstrap of the…
In this paper we present a tail inequality for the maximum of partial sums of a weakly dependent sequence of random variables that are not necessarily bounded. The class considered includes geometrically and subgeometrically strongly mixing…